Form invariance for systems of generalized classical mechanics

doi:10.1088/1009-1963/12/10/303

中国物理B ›› 2003, Vol. 12 ›› Issue (10): 1058-1061.doi: 10.1088/1009-1963/12/10/303

Form invariance for systems of generalized classical mechanics

梅凤翔¹, 张毅²

(1)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Civil Engineering, University of Science and Technology of Suzhou, Suzhou 215011, China

收稿日期:2003-03-19 修回日期:2003-04-19 出版日期:2003-10-16 发布日期:2005-03-16
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the "Qing Lan" Project Foundation of Jiangsu Province, China.

Form invariance for systems of generalized classical mechanics

Zhang Yi (张毅)^a, Mei Feng-Xiang (梅凤翔)^b

^a Department of Civil Engineering, University of Science and Technology of Suzhou, Suzhou 215011, China; ^b Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China

Received:2003-03-19 Revised:2003-04-19 Online:2003-10-16 Published:2005-03-16
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the "Qing Lan" Project Foundation of Jiangsu Province, China.

摘要/Abstract

摘要： This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. According to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and establishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is given to illustrate the application of the results.

Abstract: This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. According to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and establishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is given to illustrate the application of the results.

Key words: system of generalized classical mechanics, canonical equation, form invariance, Lie symmetry, Noether symmetry

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.30.Hq (Ordinary differential equations) 02.20.Sv (Lie algebras of Lie groups)

张毅, 梅凤翔. Form invariance for systems of generalized classical mechanics[J]. 中国物理B, 2003, 12(10): 1058-1061.

Zhang Yi (张毅), Mei Feng-Xiang (梅凤翔). Form invariance for systems of generalized classical mechanics[J]. Chinese Physics, 2003, 12(10): 1058-1061.

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Form invariance for systems of generalized classical mechanics

Form invariance for systems of generalized classical mechanics

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